If nature be regarded as the teacher and we poor human beings as her pupils, the human race presents a very curious picture. We all sit together at a lecture and possess the necessary principles for understanding it, yet we always pay more attention to the chatter of our fellow students than to the lecturer's discourse. Or, if our neighbor copies something down, we sneak it from him, stealing what he himself may have heard imperfectly, and add it to our own errors of spelling and opinion.
I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.
The lower classes of men, though they do not think it worthwhile to record what they perceive, nevertheless perceive everything that is worth noting; the difference between them and a man of learning often consists in nothing more than the latter's facility for expression.
The natural scientists of the previous age knew less than we do and believed they were very close to the goal: we have taken very great steps in its direction and now discover we are still very far away from it. With the most rational philosophers an increase in their knowledge is always attended by an increased conviction of their ignorance.
Those who have racked their brains to discover new proofs have perhaps been induced to do so by a compulsion they could not quite explain to themselves. Instead of giving us their new proofs they should have explained to us the motivation that constrained them to search for them.
One cannot demand of a scholar that he show himself a scholar everywhere in society, but the whole tenor of his behavior must none the less betray the thinker, he must always be instructive, his way of judging a thing must even in the smallest matters be such that people can see what it will amount to when, quietly and self-collected, he puts this power to scholarly use.
We often have need of a profound philosophy to restore to our feelings their original state of innocence, to find our way out of the rubble of things alien to us, to begin to feel for ourselves and to speak ourselves, and I might almost say to exist ourselves.